2. What movement of my hand will cause the mass on the spring to become unstable, slow, medium or fast?

3. Free vibrations
Every oscillator has a natural frequency of vibration. This is the frequency with which an oscillator vibrates at after an initial disturbance.
Observe how the oscillations, f0 change when the driving frequency, f changes.
f << f0
f = f0
f >> f0

5. Forced vibrations Are these oscillations free or forced?
This is where an object has been forced to vibrate at a particular frequency.
Are these oscillations free or forced?

6. An oscillator can be forced to vibrate with increasing amplitude; to do this; energy must be supplied in the right way.
A child on a park swing is the classic example that all can visualise. The push must come at the same frequency as the natural frequency of the oscillating object and at the right point in the it’s cycle.
So the energy input system must be ‘tuned’ to the oscillator, or the oscillator must be able to be tuned to the available energy input. Matching up the natural frequency and the forcing frequency results in a resonant system. The fundamental resonant frequency is synonymous with the natural frequency of an oscillator.
Resonance can lead to very large oscillation amplitudes that can result in damage. E.g. buildings etc need to have their natural frequency very different from the likely vibration frequencies due to earthquakes.
Tacoma Narrows Bridge Russian bridge Millenium Bridge

8. Youtube link http://www. youtube. com/watch

9. Resonance video
Resonance video 2, salt patterns

11. Resonance and Phase
At resonance the driver is one quarter of a cycle (π /2) ahead of the driven oscillator
If fdriver<fnat then driver and driven are nearly in phase.
If fdriver>fnat then driver and driven are nearly in antiphase.
Link to video of Barton’s pendulums showing phase differences

12. Resonance
Car panels are padded to avoid annoying rattles at certain speeds.
High frequency, large amplitude vibrations in helicopters can resonate a pilot’s skull and blur vision.
Many wind instruments use resonance of the air column.
Digital timers use the natural frequency of a quartz crystal for accurate timing.
Radios and tvs are tuned to the right frequency by a resonant (capacitor-inductor) circuit.
MRI scanners identify radio waves emitted by the resonant oscillations of certain molecules.
Microwave ovens emit at a frequency that matches the natural frequency of water molecules, so food containing water absorbs that energy most effectively, glass and plastic don’t. Less energy is wasted heating up the containers.

13. Resonance can be good
Link to video of 2D stationary wave

14. MRI Scan

15. Tuning a radio

16. Resonance can be bad!
Wikipedia link
Tacoma Narrows
Click for video

17. Angers Bridge, also called the Basse-Chaîne Bridge, was a suspension bridge over the Maine River in Angers, France. It was built between 1836 and The bridge collapsed on April 16, 1850, while a battalion of French soldiers was marching across it, killing over 200 of them.
The bridge spanned 102 m, with two wire cables carrying a 7.2 m wide deck. Its towers consisted of cast iron columns 5.47 m tall
The bridge’s amplitude of vibration exceeded the permissible limits of strength and the bridge collapsed. Other similar cases of bridges falling down have been reported. Since that time soldiers are forbidden to cross the bridges marching in step.

18. Damping

19. Shock absorbers Link to excellent animation
At the M.O.T. garage, the mechanic tests the damping of your shock absorbers by 'bouncing' the wings of the car...he probably doesn't know he is measuring Q-factor, but he does know that more than a 'bounce-and-a-half' and it fails!

20. Damping

21. Resonance Curves with increasing levels of damping
Resonance Curves with increasing levels of damping. With increased damping, the peak of resonance decreases
Which curve shows a more heavily damped system?

22. The peak in (b) is lower and broader, and it is the width of the peak that gives us a measure of damping.
With greater damping there will be less of a resonant effect, but it will happen over a larger range of frequencies.

23. Damping a moving coil meter
Damping a moving coil meter. Reading a meter would be very frustrating if it kept oscillating about the true reading (underdamped), or if it took ages to get to it (overdamped). Critical damping gets to the correct reading in the minimum time.

24. Increased damping reduces the resonant amplitude, but also causes a slightly lower resonant, just below the natural frequency.

25. Heavily damped Lightly damped
Undamped (ζ = 0): The system oscillates at its natural resonant frequency (ωo).
This is used in clocks.
Underdamped (0 < ζ < 1): The system oscillates at lower frequency
Than the undamped case with the amplitude gradually decreasing to zero.
Critically damped (ζ = 1): The system returns to equilibrium as quickly
as possible without oscillating. This is often desired for the damping of
systems such as fire-doors and car suspension.
Overdamped (ζ > 1): The system returns exponentially to equilibrium without oscillating. Larger values of the damping ratio ζ return to equilibrium more slowly.
How is the system on the right damped? damping ratio ζ

26. Damping sound vibrations
Computer Noise Dampening Material

27. Base Isolation and Vibration Damping Products